I have updated the tertation for small b . The minimal of quasi-periods determines the periodicity; the side of longest quasiperiod (negarive real part) has cuts of analyticity. Please, indicate the first statement you consider as "not explained".

Good with the accompanying text it becomes clear.
One minor correction: In the left part of fig. 2 its not but as the period is purely imaginary. Did you btw play around with other complex fixed points, differently from the one nearest the real axis? For the distribution of fixed points I even created a small "movie" here.

Quote:Please, enter into my code, extract few values and compare with yours.

But you didnt give me your code yet! I have the code for fig. 2 and the example of the contourplot.

Quote:You have no need to work much inside the "conto" function; the only, may be, suppress the message about "Copyleft"; it will run even faster. (just type // at the beginning of line). Map your tetration with my conto plotter.

Attached is the somewhat ameteurish result for base . The red lines are .